Trig Identity Problem

**Daniels4691** · May 14th 2009, 08:01 PM

Just started trig, please show step by step.
1> cos 19pi / 12 using Half-Angle Identites

2> cos 165* using Half-Angle Identites

any help would be greatly appreciated!

**skeeter** · May 15th 2009, 07:12 AM

Originally Posted by Daniels4691

Just started trig, please show step by step.
1> cos 19pi / 12 using Half-Angle Identites

2> cos 165* using Half-Angle Identites

any help would be greatly appreciated!

$\cos\left(\frac{x}{2}\right) = \pm \sqrt{\frac{1 + \cos{x}}{2}}$

in addition to the half-angle identity, you need the folowing information ...

$\frac{19\pi}{12}$ is in quadrant IV, which tells you the sign of the cosine value.

$\frac{19\pi}{12}$ is half of $\frac{19\pi}{6}$

$\frac{19\pi}{6}$ is coterminal with $\frac{7\pi}{6}$ , which means their respective cosine values are the same.

$\cos\left(\frac{7\pi}{6}\right)$ is a unit circle value.

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